This paper deals with proposing a gradient based iterative method depending upon hierarchical identification principle for solving the generalized coupled Sylvester tensor equations. To improve its performance, we further derive a modified gradient based iterative method by applying the information of previous steps. Theoretical analysis shows that the proposed methods are convergent to an exact solution for any initial value under some assumptions. Numerical examples are provided to illustrate the feasibility and validity of the methods proposed.

hierarchical identification principal, gradient based iterative method, generalized coupled Sylvester tensor equations, modified gradient based iterative method.

Received: October 29, 2021; Accepted: November 29, 2021; Published: December 8, 2021

How to cite this article: Xing-Jian Ren and Tao Li, Finding iterative algorithms for solving generalized coupled Sylvester tensor equations, JP Journal of Algebra, Number Theory and Applications 53(1) (2022), 45-68. DOI: 10.17654/0972555522003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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